A handshake message includes a field containing random data that is filled with data used to derive keying material on the source and destination computers. The data may be elliptic curve data and may include a representation of the data used by the destination computer to verify that elliptic curve data is present. The data may additionally include data for deriving second keying material on a second destination computer that the first destination computer forwards to the second computer, receives a response, and returns data from the response as part of its own handshake message.